National Geophysical Data Center candidate for the World

Digital Magnetic Anomaly Map
S. Maus and T. Sazonova
CIRES at the University of Colorado and NOAA’s National Geophysical Data Center, 325 Broadway, Boulder,
Colorado 80305-3328, USA (stefan.maus@noaa.gov)
K. Hemant
Goddard Space Flight Center, Greenbelt, Maryland 20770, USA
J. D. Fairhead
GETECH, University of Leeds, LS2 9JT Leeds, UK
Dhananjay Ravat
Department of Geology, Southern Illinois University, Mail Stop 4324, Carbondale, Illinois 62901, USA
[1] Marine and airborne magnetic anomaly data have been collected for more than half a century, providing
global coverage of the Earth. Furthermore, the German CHAMP satellite is providing increasingly accurate
information on large-scale magnetic anomalies. The World Digital Magnetic Anomaly Map project is an
international effort to integrate all available near-surface and satellite magnetic anomaly data into a global
map database. Teams of researchers were invited to produce candidate maps using a common pool of data
sets. Here we present the National Geophysical Data Center (NGDC) candidate. To produce a
homogeneous map, the near-surface data were first line-leveled and then merged by Least Squares
Collocation. Long wavelengths were found to agree surprisingly well with independent satellite
information. This validates our final processing step of merging the short-wavelength part of the near-
surface data with long-wavelength satellite magnetic anomalies.
Components: 5515 words, 5 figures, 1 table.
Keywords: geomagnetic field; crustal field; satellite geomagnetism; aeromagnetic survey; marine magnetic data.
Index Terms: 1545 Geomagnetism and Paleomagnetism: Spatial variations: all harmonics and anomalies; 1541
Geomagnetism and Paleomagnetism: Satellite magnetics: main field, crustal field, external field; 1532 Geomagnetism and
Paleomagnetism: Reference fields: regional, global.
Received 23 March 2007; Accepted 12 April 2007; Published 29 June 2007.
Maus, S., T. Sazonova, K. Hemant, J. D. Fairhead, and D. Ravat (2007), National Geophysical Data Center candidate for the
World Digital Magnetic Anomaly Map, Geochem. Geophys. Geosyst., 8, Q06017, doi:10.1029/2007GC001643.
1. Introduction
[2] Magnetic anomaly maps derived from ship and
airborne surveys have played a key role in devel-
oping the theory of plate tectonics [Wegener, 1912;
Vine and Matthews, 1963] and unraveling the
structure of the Earth’s lithosphere [Phillips et al.,
1991]. Stitching together large numbers of surveys,
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Q06017, doi:10.1029/2007GC001643
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magnetic anomaly maps have been produced for all
of the continents [Fairhead et al., 1997; Minty et
al., 2003]. Furthermore, a large marine magnetic
track line database is being maintained at the
National Geophysical Data Center (http://www.ngdc.
noaa.gov/mgg/geodas/trackline.html).
[3] These marine track line data provide a reason-
ably dense coverage of ocean areas, although
sparse data in parts of the southern oceans remain
a serious limitation for global mapping.
[4] A key issue in producing a global map is the
control of the longest wavelengths [Ravat et al.,
2002]. Magnetic anomalies with wavelengths of
more than a few hundred kilometers are not reli-
ably determined by stitching together near-surface
airborne and marine data. Only satellites can pro-
vide the global perspective. The POGO (1967–
1971) and Magsat (1979–1980) missions proved
that the lithospheric magnetic field is indeed dis-
cernible at satellite altitude. However, due to high
noise levels and eccentric orbits, lithospheric field
models derived from the early satellite data by
different techniques disagreed considerably [Cain
et al., 1989; Ravat et al., 1995; Cohen and
Achache, 1990]. A breakthrough was achieved
with the CHAMP satellite [Reigber et al., 2002],
launched in July 2000. With its high-accuracy
instrumentation and long life at low orbital alti-
tudes, CHAMP has made it possible for the first
time to accurately map large-scale magnetic
anomalies in the 400 km to 2500 km waveband
[Maus et al., 2002, 2007]. Indeed, with CHAMP
operating at continuously decreasing altitude, res-
olution may improve to 300 km in coming years.
This information on the long wavelength field is
essential for integrating regional data into a global
anomaly map.
[5] The final step of producing such a global
magnetic anomaly map is only now being under-
taken in a concerted effort, lead by a task force of
the International Association for Geomagnetism
and Aeronomy (http://www.ngdc.noaa.gov/IAGA/
vmod/). The aim of this effort is to produce a World
Digital Magnetic Anomaly Map (WDMAM). The
task force has asked all organizations holding
marine and aeromagnetic data to contribute track
line data and 5 km resolution grids to the WDMAM
project. This call for data has been encouragingly
successful, with good coverage of near-surface data
now available for the first version of the WDMAM,
to be unveiled at the International Union for Geo-
physics and Geodesy (IUGG) General Assembly in
Perugia, Italy, in July 2007. In order to arrive at a
high-quality scientific product, a call for candidate
models for WDMAM was issued in June 2006,
and six candidates were submitted to the task force
in November 2006 for evaluation. The candidate
models were produced by teams at the Geological
Survey of Finland (GTK), NASA, University of
Leeds, GeoForschungszentrum Potsdam (GFZ),
and NGDC. Following evaluations by internal
and external reviewers, the NGDC candidate was
selected by the WDMAM task force as a base
map, to undergo further modifications by the other
teams. The resulting community map will be
distributed as the official WDMAM in print and
digital form by the Commission for the Geological
Map of the World. This paper describes the
NGDC candidate, produced by the authors of this
paper.
2. Methods
[6] The guiding principles for our processing
methodology were (1) to provide the most accurate
estimate of the lithospheric magnetic field on the
final grid and (2) to produce a homogeneous grid
whose horizontal derivatives were dominated by
geological features rather than by data artifacts. In
implementing the second goal, we accepted that the
resulting product would be somewhat smoother
than the actual lithospheric magnetic field. Two
methods were used here which require further
explanation. The first is a Least Squares Colloca-
tion method [Moritz, 1980] which we used to
generate a grid from arbitrarily located input mea-
surements. The second is a line-leveling method
[Paterson and Reeves, 1985] used to correct for
random offsets between track lines.
2.1. Least Squares Collocation
[7] The WDMAM grid is defined as the magnetic
field anomaly at an altitude of 5 km above the
WGS84 reference ellipsoid with an angular reso-
lution of 3 arc minutes. Future versions of the
WDMAM may be defined at a higher resolution
and lower altitude. Since the locations of the given
measurements are usually not identical to the
WDMAM grid nodes, one requires a procedure
to estimate the field at those nodes. In principle,
there appear to be at least two ways of achieving
this. The first is to use a Fourier method. However,
a Fourier approach assumes plane geometry, can
produce edge effects, cannot handle track line data,
has to be specifically adapted to draped surveys
(varying survey altitude), and cannot simulta-
neously handle several data sets. Instead, we
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therefore used Least Squares Collocation (LSC), a
popular method in geodesy [Moritz, 1980]. With
the LSC method one can directly estimate the
magnetic field at a desired location and altitude,
taking into account all neighboring magnetic field
measurements. The use of LSC for magnetic field
studies is described well in the book of Chapter
5.3.3 Langel and Hinze [1998] and can be sum-
marized as follows:
[8] The goal is to estimate a vector of magnetic
anomaly field values b at a number of different
locations, given a vector of magnetic anomaly
measurements c at surrounding locations with
possibly different altitudes. The measurement vec-
tor can be thought of as the sum of the true
anomaly vector a plus an error vector e. One has
to take into account the horizontal and vertical
separation of the measurements from the locations
at which b is to be estimated. For this purpose, one
makes a statistical assumption on how the field
behaves with horizontal and vertical separation.
Langel and Hinze [1998, chap. 5.3.3, p. 137]
propose two correlation functions which they call
V
2
and V
3
. The model correlation functions V
2
and
V
3
are given by
V
2
d
1;2
; z
1
; z
2

¼ V
0
b d
2
1;2
þ z
1
þz
2
þb ð Þ
2

À1=2
;
b ¼ r
c
=
ﬃﬃﬃ
3
p
V
3
d
1;2
; z
1
; z
2

¼ V
0
b
2
z
1
þz
2
þb ð Þ
Á d
2
1;2
þ z
1
þz
2
þb ð Þ
2

À3=2
;
b ¼ r
c
=0:766
where d
1,2
is the horizontal separation and z
1
and z
2
are the vertical coordinates of two locations 1 and 2.
Both correlation functions have two free para-
meters, the variance V
0
and the correlation length r
c
.
The parameter V
0
is just a linear scale factor for the
y axis, while r
c
can be interpreted as a scale factor
on the x axis. Scaling along the x axis is further
influenced by the altitude of the measurement and
grid locations, reflecting the fact that a larger
correlation length of the sources and a larger
vertical distance to the sources both lead to a
smoother field.
[9] The correlation function V
3
falls off more
rapidly with distance than V
2
. Since magnetic
anomaly fields are generally less smooth than
gravity fields, it seemed likely that the function
V
3
would turn out to be more suitable for magnetic
anomaly modeling, which was confirmed in the
following analysis. To verify the suitability of V
2
and V
3
and to estimate V
0
and r
c
, we computed the
empirical correlation functions for some arbitrarily
chosen rectangular areas in the NGDC magnetic
grid of the former Soviet Union, the Australian and
the North American magnetic anomaly grids (see
Table 1). The correlation functions are displayed in
Figure 1. We find that V
3
gives a better fit than V
2
.
By trial and error, we infer values of V
0
=
40,000 nT
2
and r
c
= 15 km which are used for
all locations.
[10] The least squares estimate b of the vector of
anomalies b is then given by
b ¼ V
T
a;b
V
À1
c
c ð3Þ
where the matrix V
a,b
is defined as
V
a;b
¼ V
3
d
a;b
; z
a
; z
b

ð5Þ
evaluated for all pairs of measurements. Here,
E(ee
T
) is the expected error co-variance matrix.
The beauty of this term is that it allows to specify
correlated errors for data within the same data set.
Such correlated errors are due to systematic offsets
between neighboring tracks, or between a track and
a grid. In fact, such offsets are the dominant
uncertainties in the data. We assumed that (after
line leveling) the uncorrected offset is 25 nT, and
that this is the primary source of error. Thus we
chose
E ee
T

¼
625 nT
2
for data pairs from the same set
0 nT
2
for data pairs from different sets:

ð6Þ
In summary, the LSC method allows for the
optimal estimation of a grid from multiple data
sets taking into account different survey altitudes
and random offsets between data sets.
2.2. Line Leveling of Marine and
Airborne Track Line Data
[11] Even under the optimum conditions of a single
aeromagnetic survey with ground reference sta-
tions, track lines end up having random offsets.
In aeromagnetic surveys, these are corrected using
ð1Þ
ð2Þ
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perpendicular tie lines [Paterson and Reeves,
1985]. The marine track line data used for the
WDMAM is much more prone to this kind of error.
In addition, the older data may have navigational
errors, a problem which is addressed later by
rejecting incompatible track segments. The data
are measured over a time span of 50 years, some-
times thousands of kilometers away from the
nearest magnetic observatory. Apart from incom-
pletely removed main and external fields, there are
also likely to be instrument biases. The resulting
uncertainty in the longer wavelength part of the
magnetic field can be dealt with by line leveling,
which minimizes the misfit between neighboring or
crossing tracks.
[12] To each track with index i we assign a cor-
rection function
f
i
d ð Þ ¼
¸
Ni
k¼0
a
i;k
cos pkd=D
i
ð Þ ð7Þ
where D
i
is the great circle distance from the first
to the last point of the track and N
i
is the number of
parameters used for the correction function of the
track. We use N
i
= trunc(D
i
/400 km) + 1. Thus we
roughly assume that all information in the track
with a half-wavelength exceeding 400 km is
unreliable and is subject to adjustment in the line
leveling. In one grand inversion, we then estimated
the optimum parameters a
i,k
, which minimize the
misfit between all neighboring tracks and simulta-
neously minimize the misfit of the track line to the
gridded data. In this procedure the gridded data are
not modified. To account for the distance between
Table 1. Summary of Data Sets, With Their Official WDMAM Codes, Coverage, and References
a
Code Area Covered Res Reference
701.43 North America 1 km NAMAG, http://pubs.usgs.gov/sm/mag_map/
302.43 Antarctica 5 km ADMAP, http://www.geology.ohio-state.edu/geophys/admap/
504.43 Australia 1 km Geoscience Australia, http://www.ga.gov.au/
601.43 Europe 5 km Wonik, BGR, http://www.bgr.bund.de/
121.43 Arctic 5 km GSC, http://gsc.nrcan.gc.ca/index_e.php
421.43 Middle East 1 km AAIME, http://home.casema.nl/errenwijlens/itc/aaime/
411.43 East Asia 2 km CCOP, http://www.ccop.or.th/
442.2 India 50 km Qureshy [1982]
441.3 India 5 km GSI, http://www.gsi.gov.in/
201.2 Africa 15 min GETECH, http://www.getech.com/
201.2 S. America 15 min GETECH, http://www.getech.com/
625.2 France 10 km IPGP, http://www.ipgp.jussieu.fr/
627.43 Spain 1.5 min Socias et al. [1991]
222.3 South Africa 5 km SADC, http://www.sadc.int/
611.3 Fennoscandia 5 km GTK, http://www.gtk.fi/
626.2 Italy 5 km Chiappini et al. [2000]
622.2 Canary Islands 5 km Socias and Mezcua [1996]
812.3 Argentina margin 5 km Ghidella, DNA, http://www.dna.gov.ar/
811.45 Argentina inland 5 km SEGEMAR, http://www.segemar.gov.ar/db/
401.3 Eurasia 2 km GSC, http://gsc.nrcan.gc.ca/index_e.php
628.3 Russia 5 km VSEGEI, http://www.vsegei.ru/WAY/247038/locale/EN
101.45 Marine track line variable NGDC, http://www.ngdc.noaa.gov/mgg/geodas/trackline.html
131.45 Project Magnet variable NGDC, http://www.ngdc.noaa.gov/seg/geomag/proj_mag.shtml
a
Some resolutions (Res) are given in arc minutes (min).
Figure 1. Observed correlation functions, computed
from arbitrary rectangular areas in the NGDC magnetic
grid of the former Soviet Union and the Australian and
the North American magnetic anomaly grids. Overlain
are the model correlation functions of equations (1) and
(2), assuming a uniform survey altitude of 1000 m. The
model V
3
gives a better fit than V
2
.
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measurement locations in computing the misfit, we
use the weight function
W d
1;2
; z
1
; z
2

ð8Þ
where R
s
= 100 km is the search radius, and d
1,2
, z
1
and z
2
are again the horizontal separation and the
vertical coordinates, respectively. In this definition
of the weight function, the vertical separation is
upweighted by a factor 2 in order to account for the
greater variability of a poloidal field in the vertical
than in the horizontal direction.
3. Input Data
[13] The input data fall into three different catego-
ries: (1) marine and aeromagnetic track line data,
(2) large-scale aeromagnetic and marine magnetic
grids, and (3) CHAMP satellite data which are
included in form of the MF5 model [Maus et al.,
2007]. The data sets are listed in Table 1.
4. Data Processing Steps
[14] Our data processing scheme starts with com-
bining the existing grids to a single common grid,
then preparing the track line data and merging them
to a combined grid, and finally replacing the
longest wavelengths with MF5.
4.1. Gridded Data
[15] Most aeromagnetic surveys over land have
already been combined to country-wide or even
continental compilations. These compilations are
mostly very well made, and it would be far beyond
the scope of the WDMAM project to locate and
reprocess individual surveys that contributed to
these large-scale compilations.
[16] In some cases, areas are covered by several
compilations. If in such cases one of the compila-
tions is known to have superior resolution or
accuracy, overlapping parts of the lower quality
grids were discarded. This applies to (1) the 50 km
resolution ground magnetic survey of India
(code 442.2), which is partly covered by the 5 km
resolution aeromagnetic map of India (code 441.3),
(2) the GSC compilation of Eurasia (code 401.3),
which is partly covered by the new Russian grid
(code 628.3), and (3) the 15 arc minute GETECH
dat a of South Ameri ca, Afri ca and Asi a
(code 201.2), which are partly covered by various
smaller 5 km resolution grids.
[17] In order to avoid the possible loss of informa-
tion in the following processing steps, we resampled
all grids to 1.5 arc minute angular resolution
using the minimum curvature algorithm (program
‘‘surface’’) of Generic Mapping Tools (GMT)
[Wessel and Smith, 1991].
[18] The LSC method takes into account the exact
altitude of the measurements. Some compilations
are provided at barometric altitude. However, most
compilations are draped, meaning that they follow
the surface topography at a constant altitude above
terrain. For the accurate processing of the altitude
information, one therefore requires a topographic
model of the Earth. We used NGDC’s ETOPO-2
surface elevation grid (http://www.ngdc.noaa.gov/
mgg/global/global.html), which we linearly inter-
polated to the measurement positions and added to
the terrain clearance of all draped surveys, in order
to compute the measurement altitude above the
geoid.
[19] In the merging of the compilations, random
offsets between neighboring and overlapping grids
must be adjusted. These random offsets reflect
inherent uncertainties at long wavelengths, caused
by stitching together small-scale surveys. To deal
with such edge effects, we first subtracted a linear
2D trend from all smaller size grids. Then we
computed the distance to the nearest margin for
all points of every grid. Finally, we merged the
grids by LSC (see section 2), using weights which
are linearly proportional to the distance from the
margin, starting at 0.01 on the margin and extend-
ing to a maximum value of 1.0 for 200 km inland.
This procedure may introduce spurious anomalies
with half-wavelengths larger than 200 km. How-
ever, these spurious anomalies are largely removed
at a later stage, when the long wavelengths are
substituted with the MF5 model.
4.2. Track Line Data
[20] Short wavelength noise in marine and aero-
magnetic track line data is mostly caused by
external fields. Identifying such disturbed sections
is a challenging task. In particular, genuine crustal
anomalies can exceed strengths of 1000 nT, while
external field disturbances with amplitudes of
100 nT already give rise to spurious magnetic
anomalies. Thus disturbed sections cannot be iden-
tified by residual amplitude. However, ships and
aircraft move relatively slowly, while strong exter-
nal field disturbances change rather rapidly. We
therefore used the along-track derivative of the
magnetic field residual as a selection criterion. If
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the derivative exceeded 100 nT/km, the 20 preced-
ing and following measurement points were dis-
carded. The threshold of 100 nT for the along-track
gradient was found by trial and error, using a test
area with strong ocean magnetic anomalies in the
North Pacific. This threshold eliminated about 3%
of the marine track line data and 9% of the Project
Magnet data. It is not clear why the Project Magnet
data seemed noisier than the marine data. In fact,
one may have expected the opposite. This surpris-
ing discrepancy in data quality will have to be
investigated in the run-up to the next edition of the
WDMAM.
[21] In order to reduce the huge volume of data, the
track line data were resampled by averaging in
2.5 km bins. For the subsequent line leveling, the
data were further broken into straight segments.
The NGDC marine data consist of about 20 million
points on 28,000 tracks, which we broke into
91,000 segments and resampled to 4 million points.
Similarly, 7 million Project Magnet measurements
on 3000 tracks were broken up into 7,000 segments
and resampled to 800,000 points.
[22] Using the procedure described in section 2, we
then line-leveled the 98,000 track segments against
each other by estimating 110,000 correction coef-
ficients which simultaneously minimized offsets
where tracks overlap with the gridded data. After
leveling, plotting the misfits reveals some large
outliers of segments which could not be brought
into agreement with the other data. This is expected
for segments with strong external disturbances or
segments with incorrect positions due to navigation
errors. After visual inspection of the distribution of
misfits, we discarded the segments with a remain-
ing between-segment misfit exceeding 550 nT, or a
misfit against the gridded data exceeding 500 nT.
This removed about 1% of the segments. The
leveling and selection reduced the root-mean-
square (rms) between-segment misfit from 380 nT
to 130 nT (i.e., 81 nT if only exact cross-overs are
counted) and the misfit against the gridded data
from 400 nT to 90 nT.
[23] Finally, the leveled line data were merged with
the gridded data, again using the LSC method,
taking into account the altitude of the ship-borne
and Project Magnet data.
[24] An example of the effect of line leveling and
the final merge is shown in Figure 2. The left panel
shows the raw track line data, the middle shows the
leveled and selected data, while the right panel
shows the final map after merging with the gridded
data and long-wavelength substitution. Several
interesting inferences can be made from this figure.
The first is that the input data are indeed seriously
offset against each other. This is mostly due to the
Earth’s changing main magnetic field, and the
limited accuracy of the reference fields used for
the original main field corrections. However, these
offsets are of long wavelength and are removed by
Figure 2. Processing and merging of track line and gridded data, illustrated for Central America. The left panel
shows the raw marine and aeromagnetic data. Line leveling and discarding tracks with remaining high offsets lead to
the middle panel. Finally, the merger with the gridded data (which also cover parts of the oceans) and the correction
of the long wavelengths with the satellite model MF5 lead to the final result shown in the right panel.
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the line leveling, as seen in the middle panel. A
problem in the line leveling is exposed for the
Cayman trough, where the track line data of an
entire area were rejected because they exceeded the
rms threshold. This should probably not have
happened and needs to be investigated prior to
the next map edition. Fortunately, this omission
had only a limited impact on the final map because
the area is covered by the North American compi-
lation. Adding the North American compilation
introduced new problems, however: Off the Pacific
coast of Central America (Figure 2, middle panel)
one can see convincing small-scale linear features
trending southeast. Unfortunately, these features
are strongly suppressed when adding on the North
American compilation. This observation also holds
in other ocean areas, where line-leveled marine
data often provide more accurate information than
the compilations, although they were produced
largely from the same original measurements.
4.3. Substituting the Longest Wavelengths
With a CHAMP Satellite Model
[25] Long wavelengths in grid and track line data
are known to be highly inaccurate. This is primar-
ily due to temporal changes of the main field.
Stitching together surveys and tracks collected at
different times only allows for very limited control
of wavelengths exceeding typical survey sizes of a
few hundred kilometers. These long wavelengths
are more accurately recorded by low-orbiting sat-
ellites. Since 2000, the CHAMP satellite has been
measuring the magnetic field with unprecedented
accuracy. Here, we used the lithospheric field
model MF5 [Maus et al., 2007], estimated from
the latest three years of CHAMP data from August
2003 through July 2006.
[26] There are several ways to replace the long
wavelengths of the combined grid with MF5 in the
spectral domain. We chose a processing route via
the magnetic potential. A total intensity data cov-
erage on the sphere does not completely constrain
the magnetic potential [Backus, 1970]. The ambi-
guity is further increased by the incomplete data
coverage. By using the least squares method and
eliminating the lowest Eigenvalues, one can select
one of many magnetic potentials that represent the
observed anomaly. We computed this magnetic
potential of the near-surface data to degree 120.
Figure 3 shows the degree correlation between this
model and MF5. If the coefficients of one model
are denoted by g
n
m
and the other by k
n
m
the corre-
lation as a function of degree n is defined here
following Langel and Hinze [1998, equation
(4.23)] as
C n ð Þ ¼
¸
m
g
m
n
k
m
n
¸
m
g
m
n

2
¸
m
k
m
n

2

1=2
ð9Þ
Note that the two data sources are completely
independent. No satellite data have been used in
our grid, neither for the track line data nor the
gridded data. In particular, we used the original,
unfiltered NAMAG grid, rather than one of its
modifications where long wavelengths were sub-
stituted with satellite magnetic models. The
correlation increases to an encouragingly high
value of about 0.6 at degree 100, validating the
high-degree coefficients of MF5. Indeed, the high
correlation indicates that valuable small-scale
signal is contained in the satellite data beyond
degree 100. One could even argue that MF5 should
have been expanded up to the degree where the
correlation peaks before decreasing to zero. We
will take note of this when producing the next
generation satellite lithospheric model MF6.
[27] Another important check before replacing the
long wavelengths with MF5 is to see how well
their power spectra agree. Figure 4 shows the near-
surface data spectrum in comparison with MF5.
The near-surface data exhibit strong low-degree
power, caused by unremoved main field in the
continental scale grids. At high degrees, however,
the power of the near-surface data is only about
10% higher than MF5. Again, considering the
different data sources and the multitude of process-
ing steps and corrections, a disagreement of 10% in
Figure 3. Degree correlation, as defined by equation (9),
between the satellite-only model MF5 and our model
from the merged near-surface data. Considering the
completely different nature of the two data sets, the
correlation is surprisingly high.
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power (which amounts to even less in amplitude) is
encouragingly small. It is difficult to pin-point the
source of this discrepancy which is probably a mix
of several effects. The prime candidate for a lack of
power in MF5 is the removal of genuine field in the
rigorous processing of the satellite data, while
excess power in the near-surface data at 400 km
wavelength could be due to spurious large-scale
features introduced in the stitching together of
small-area surveys.
[28] Given the good spectral agreement between
MF5 and the near-surface model at degree 100, we
use a sharp cut-off to substitute the long wave-
lengths of the near-surface data with the MF5
model. This substitution was carried out by sub-
tracting the near-surface model to degree 100 from
each grid cell and then adding the prediction from
MF5.
4.4. GIS Flags
[29] The format definition of the WDMAM grid
includes a fourth column identifying the primary
data source of each grid cell. This information is of
course not unique in areas of overlapping data sets.
We decided that gridded data should have priority
over track line data, reflecting the line leveling
onto the gridded data. As mentioned above, we had
discarded areas of the lower-resolution grids which
were covered already by higher-resolution grids. In
remaining overlap areas, our present flagging is
somewhat arbitrary. In future map editions a hier-
archy of the different data sets based on data
resolution and accuracy should be assigned.
5. Result
[30] The final result (Figure 5) of the processing is
a three arc minute angular grid of the total intensity
anomaly at 5 km above the WGS84 geoid. In the
grid, unsurveyed areas are filled with the satellite-
only model MF5 and flagged with code 13. It
should be noted, however, that plotting these fill-
in values as part of the map can lead to serious
misinterpretation since it is then unclear whether
the field is smooth because of the geologic setting
or because of inadequate data coverage. This
problem is particularly obvious in the southern
Indian Ocean, where the mid ocean ridge stands
out clearly as a positive anomaly. This occurs not
because the ridge is particularly magnetic, but
because it is the only well-surveyed area in the
region. Most likely, there are equally strong paral-
lel patterns, but in the absence of measurements the
grid defaults to the smooth MF5 model. Such
misinterpretation is avoided if the fill-in values
are not plotted as part of the map. We therefore
prefer to plot the field only for areas where near-
surface data are available. This has the additional
advantage of showing where further data are need-
ed for future WDMAM editions, hopefully moti-
vating new data collection efforts.
[31] In plotting the final map (Figure 5), we find
that there is a technical difficulty in displaying
single track lines. Ideally, the lines should be
equally broad for North/South and East/West ori-
ented tracks. However, due to anisotropic stretch-
ing in global projections track line widths are
distorted. With the Generic Mapping Tool’s Mer-
cator projection, North/South oriented tracks be-
come very wide and East/West oriented tracks
exceedingly thin. For our final map we therefore
used GMT’s Mollweide projection, which avoids
this distortion. The polar stereographic projections
did not exhibit this problem.
6. Grid Availability and Outlook
[32] The official WDMAM is expected to be re-
leased in July 2007 at the Meeting of the Interna-
tional Union of Geodesy and Geophysics in
Perugia. There will be a paper copy of the map,
as well as a DVD with the digital grid and the
candidate WDMAM submissions, to be distributed
by the Commission for the Geological Map of the
World, 77, rue Claude-Bernard, 75005 Paris,
Figure 4. Spectra of the near-surface-data spherical
harmonic model and MF5. The high power at low
degrees in the near-surface data is primarily due to
uncorrected main field. At high degrees, on the other
hand, the power levels in the two models differ only by
about 10%. The blue line shows the spectrum of the
final NGDC candidate map.
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France. The digital grid of the NGDC candidate for
WDMAM is already publicly available at http://
geomag.org/models/wdmam.html and at http://
earthref.org/cgi-bin/erda.cgi?n=735 as a permanent
archive. Furthermore, a package for visualization
of the map in NASA World Wind can be down-
loaded from http://www.getech.com/downloads/
WDMAM.
[33] The WDMAM is an ongoing project, with
plans to produce updates of the map and grid every
couple of years. As part of these updates, additional
data will be acquired for presently uncovered areas.
Some of these areas have already been surveyed but
the data are not readily accessible, for various
reasons. It is our hope that the WDMAM will enjoy
widespread usage, creating momentum to conduct
further aeromagnetic surveys and help to complete
the global coverage.
[34] Further significant improvements in accuracy
and resolution can be expected at long wavelengths
of the spatial spectrum which is supplied by low-
orbiting satellites. The CHAMP mission is expected
to continue providing excellent quality data at solar
minimum conditions and at steadily decreasing
altitudes up to the year 2009. Following in 2010
is the European Space Agency’s Swarm mission, a
constellation comprising 3 satellites (http://www.
esa.int/esaLP/LPswarm.html). This will further
improve lithospheric magnetic anomaly maps by
providing direct measurements of magnetic field
gradients [Maus et al., 2006].
[35] Thus a more complete spatial coverage by
marine and aeromagnetic data, together with better
control of the long wavelengths from new satellite
missions, offers the scope for further significant
improvements in upcoming WDMAM editions.
Acknowledgments
[36] We thank two referees, Richard Blakely and Erwan
Thebault, for numerous suggestions that helped to improve
Figure 5. The final NGDC WDMAM candidate grid. The top panel shows a Mollweide projection with cut-off at
70° latitude. The polar stereographic projections in the bottom two panels extend down to 40° in latitude.
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this manuscript. The organizations listed in Table 1 provided
marine and aeromagnetic data for the WDMAM project. We
are particularly indebted to Juha Korhonen and other members
of the WDMAM task force for their successful negotiations
with the various data providers. The work presented in this
paper was partly supported by Deutsche Forschungsgemein-
schaft in the Special Program ‘‘Geomagnetic Variations’’ (SPP
1097). The operational support of the CHAMP mission by the
German Aerospace Center (DLR) and the financial support for
the data processing by the Federal Ministry of Education and
Research (BMBF) are gratefully acknowledged.
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[4] A key issue in producing a global map is the control of the longest wavelengths [Ravat et al. Future versions of the WDMAM may be defined at a higher resolution and lower altitude. cannot handle track line data. resolution may improve to 300 km in coming years. has to be specifically adapted to draped surveys (varying survey altitude). 1997. In principle. noaa..Geochemistry Geophysics Geosystems
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maus et al.1. The aim of this effort is to produce a World Digital Magnetic Anomaly Map (WDMAM). The task force has asked all organizations holding marine and aeromagnetic data to contribute track line data and 5 km resolution grids to the WDMAM project. The first is to use a Fourier method.. In order to arrive at a
high-quality scientific product. Two methods were used here which require further explanation. Magnetic anomalies with wavelengths of more than a few hundred kilometers are not reliably determined by stitching together near-surface airborne and marine data. GeoForschungszentrum Potsdam (GFZ). a call for candidate models for WDMAM was issued in June 2006.. with good coverage of near-surface data now available for the first version of the WDMAM. However. we
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. NASA.gov/IAGA/ vmod/). Ravat et al. Instead.1029/2007GC001643
magnetic anomaly maps have been produced for all of the continents [Fairhead et al. With its high-accuracy instrumentation and long life at low orbital altitudes. In implementing the second goal. and cannot simultaneously handle several data sets. Only satellites can provide the global perspective. lithospheric field models derived from the early satellite data by different techniques disagreed considerably [Cain et al. 2003]. we accepted that the resulting product would be somewhat smoother than the actual lithospheric magnetic field.
2. 2002]. 1995.ngdc. lead by a task force of the International Association for Geomagnetism and Aeronomy (http://www.: ngdc candidate for wdmap
10. to be unveiled at the International Union for Geophysics and Geodesy (IUGG) General Assembly in Perugia. Cohen and Achache. [5] The final step of producing such a global magnetic anomaly map is only now being undertaken in a concerted effort. 1989. The second is a line-leveling method [Paterson and Reeves. CHAMP has made it possible for the first time to accurately map large-scale magnetic anomalies in the 400 km to 2500 km waveband [Maus et al. Since the locations of the given measurements are usually not identical to the WDMAM grid nodes. The candidate models were produced by teams at the Geological Survey of Finland (GTK). The POGO (1967– 1971) and Magsat (1979–1980) missions proved that the lithospheric magnetic field is indeed discernible at satellite altitude. in July 2007. due to high noise levels and eccentric orbits. This call for data has been encouragingly successful.. However. University of Leeds. produced by the authors of this paper.html). This information on the long wavelength field is essential for integrating regional data into a global anomaly map. and NGDC. Minty et al. although sparse data in parts of the southern oceans remain a serious limitation for global mapping. a large marine magnetic track line database is being maintained at the National Geophysical Data Center (http://www. Furthermore.. and six candidates were submitted to the task force in November 2006 for evaluation. The first is a Least Squares Collocation method [Moritz. Methods
[6] The guiding principles for our processing methodology were (1) to provide the most accurate estimate of the lithospheric magnetic field on the final grid and (2) to produce a homogeneous grid whose horizontal derivatives were dominated by geological features rather than by data artifacts. the NGDC candidate was selected by the WDMAM task force as a base map. This paper describes the NGDC candidate. can produce edge effects. one requires a procedure to estimate the field at those nodes. launched in July 2000. Least Squares Collocation
[7] The WDMAM grid is defined as the magnetic field anomaly at an altitude of 5 km above the WGS84 reference ellipsoid with an angular resolution of 3 arc minutes.
2.. A breakthrough was achieved with the CHAMP satellite [Reigber et al. [3] These marine track line data provide a reasonably dense coverage of ocean areas. to undergo further modifications by the other teams. 1980] which we used to generate a grid from arbitrarily located input measurements. 1990].gov/mgg/geodas/trackline. there appear to be at least two ways of achieving this.. 2007].ngdc.noaa. Following evaluations by internal and external reviewers. 2002]. a Fourier approach assumes plane geometry. Indeed. 2002. The resulting community map will be distributed as the official WDMAM in print and digital form by the Commission for the Geological Map of the World. 1985] used to correct for random offsets between track lines. with CHAMP operating at continuously decreasing altitude. Italy.

Langel and Hinze [1998.2 b ¼ rc =0:766 ð2Þ ð1Þ
following analysis. such offsets are the dominant uncertainties in the data. In fact. 1. The use of LSC for magnetic field studies is described well in the book of Chapter 5. p. and that this is the primary source of error. Á d2 þ ðz1 þz2 þ bÞ2 1.2 . Line Leveling of Marine and Airborne Track Line Data
[11] Even under the optimum conditions of a single aeromagnetic survey with ground reference stations. Such correlated errors are due to systematic offsets between neighboring tracks. z1 . Both correlation functions have two free parameters.3. z2 ¼ V0 b2 ðz1 þ z2 þ bÞ À3=2 . it seemed likely that the function V3 would turn out to be more suitable for magnetic anomaly modeling. the matrix Vc is given by
À Á À Á Vc ¼ E eeT þ V3 d1. The measurement vector can be thought of as the sum of the true anomaly vector a plus an error vector e. One has to take into account the horizontal and vertical separation of the measurements from the locations at which b is to be estimated. z1 . Here.b is defined as
À Á Va. Thus we chose
À Á E eeT ¼ & 625 nT2 for data pairs from the same set 0 nT2 for data pairs from different sets: ð6Þ
In summary. 5. which was confirmed in the
evaluated for all pairs of measurements. 1998. The parameter V0 is just a linear scale factor for the y axis.1029/2007GC001643
therefore used Least Squares Collocation (LSC). To verify the suitability of V2 and V3 and to estimate V0 and rc.2 is the horizontal separation and z1 and z2 are the vertical coordinates of two locations 1 and 2. The beauty of this term is that it allows to specify correlated errors for data within the same data set. [9] The correlation function V3 falls off more rapidly with distance than V2. We find that V3 gives a better fit than V2. or between a track and a grid. chap.2 pﬃﬃﬃ b ¼ rc = 3 À Á V3 d1. Since magnetic anomaly fields are generally less smooth than gravity fields.: ngdc candidate for wdmap
10. 1980]. In aeromagnetic surveys.
2. We assumed that (after line leveling) the uncorrected offset is 25 nT. 137] propose two correlation functions which they call V2 and V3.b . the LSC method allows for the optimal estimation of a grid from multiple data sets taking into account different survey altitudes and random offsets between data sets.3.b VcÀ1 c
ð3Þ
where the matrix Va.2 . reflecting the fact that a larger correlation length of the sources and a larger vertical distance to the sources both lead to a smoother field. By trial and error. zb .3 Langel and Hinze [1998] and can be summarized as follows: [8] The goal is to estimate a vector of magnetic anomaly field values b at a number of different locations. With the LSC method one can directly estimate the magnetic field at a desired location and altitude. track lines end up having random offsets. The correlation functions are displayed in Figure 1.2 . 136]. ð4Þ
evaluated for all pairs of estimation (b) and measurement (a) locations [Langel and Hinze.b ¼ V3 da. E(eeT) is the expected error co-variance matrix. For this purpose. the variance V0 and the correlation length rc. while rc can be interpreted as a scale factor on the x axis. we computed the empirical correlation functions for some arbitrarily chosen rectangular areas in the NGDC magnetic grid of the former Soviet Union. z2 ð5Þ
where d 1. taking into account all neighboring magnetic field measurements. a popular method in geodesy [Moritz. [10] The least squares estimate b of the vector of anomalies b is then given by
T b ¼ Va.000 nT2 and rc = 15 km which are used for all locations. Correspondingly. z1 .3. z2 ¼ V0 b d2 þ ðz1 þ z2 þ bÞ2 .Geochemistry Geophysics Geosystems
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maus et al. The model correlation functions V2 and V3 are given by
À1=2 À Á V2 d 1. given a vector of magnetic anomaly measurements c at surrounding locations with possibly different altitudes. Scaling along the x axis is further influenced by the altitude of the measurement and grid locations. za . we infer values of V0 = 40. p. the Australian and the North American magnetic anomaly grids (see Table 1). one makes a statistical assumption on how the field behaves with horizontal and vertical separation.2. these are corrected using
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2 441.2 622. Coverage.ccop.gov/sm/mag_map/ ADMAP.ca/index_e. computed from arbitrary rectangular areas in the NGDC magnetic grid of the former Soviet Union and the Australian and the North American magnetic anomaly grids. To account for the distance between
ai.edu/geophys/admap/ Geoscience Australia.: ngdc candidate for wdmap
10.gov. The marine track line data used for the WDMAM is much more prone to this kind of error. which minimize the misfit between all neighboring tracks and simultaneously minimize the misfit of the track line to the gridded data. [12] To each track with index i we assign a correction function
fi ðd Þ ¼
Ni X k¼0
leveling. In this procedure the gridded data are not modified.Geochemistry Geophysics Geosystems
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3
maus et al.php AAIME.43 421. http://gsc. http://www. Observed correlation functions. assuming a uniform survey altitude of 1000 m. http://www. http://www.geology.3 101.5 min 5 km 5 km 5 km 5 km 5 km 5 km 2 km 5 km variable variable
Reference NAMAG. The resulting uncertainty in the longer wavelength part of the magnetic field can be dealt with by line leveling.gc. http://www. The data are measured over a time span of 50 years.2 812.gov/mgg/geodas/trackline.gov/seg/geomag/proj_mag.3 626.casema. and Referencesa
Code 701.43 222. http://www.bgr.45
a
Area Covered North America Antarctica Australia Europe Arctic Middle East East Asia India India Africa S. BGR. [1991] SADC.3 201. http://gsc.43 302. http://www. DNA.fi/ Chiappini et al. With Their Official WDMAM Codes.noaa.vsegei. http://www. Summary of Data Sets. http://www. http://home.gtk.
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. Apart from incompletely removed main and external fields. http://www.45 131. 1985].ca/index_e.1029/2007GC001643
Table 1. America France Spain South Africa Fennoscandia Italy Canary Islands Argentina margin Argentina inland Eurasia Russia Marine track line Project Magnet
Res 1 km 5 km 1 km 5 km 5 km 1 km 2 km 50 km 5 km 15 min 15 min 10 km 1.ipgp.gov.43 504.gov.3 811.43 411.com/ GETECH.getech. In addition.nl/errenwijlens/itc/aaime/ CCOP. sometimes thousands of kilometers away from the nearest magnetic observatory.in/ GETECH.bund. We use Ni = trunc(Di/400 km) + 1.ohio-state.th/ Qureshy [1982] GSI.segemar.com/ IPGP.45 401.43 442.html NGDC. [2000] Socias and Mezcua [1996] Ghidella.ar/db/ GSC. which minimizes the misfit between neighboring or crossing tracks.fr/ Socias et al. The model V3 gives a better fit than V2.3 611.php VSEGEI.ngdc. there are also likely to be instrument biases.k cosðpkd=Di Þ
ð7Þ
where Di is the great circle distance from the first to the last point of the track and Ni is the number of parameters used for the correction function of the track.gc. http://www. a problem which is addressed later by rejecting incompatible track segments. http://www. the older data may have navigational errors. http://www.int/ GTK.2 625. http://www.shtml
Some resolutions (Res) are given in arc minutes (min).or.dna. http://pubs. In one grand inversion.43 121.43 601.ngdc.jussieu.usgs. Thus we roughly assume that all information in the track with a half-wavelength exceeding 400 km is unreliable and is subject to adjustment in the line
Figure 1. we then estimated the optimum parameters ai.2 627. http://www.de/ GSC.ga.au/ Wonik.sadc.gov.getech.k.2 201. Overlain are the model correlation functions of equations (1) and (2).
perpendicular tie lines [Paterson and Reeves.nrcan.ru/WAY/247038/locale/EN NGDC.noaa.ar/ SEGEMAR. http://www.nrcan.3 628.gsi.

: ngdc candidate for wdmap
10.3). genuine crustal anomalies can exceed strengths of 1000 nT. Identifying such disturbed sections is a challenging task. Track Line Data
[20] Short wavelength noise in marine and aeromagnetic track line data is mostly caused by external fields. the vertical separation is upweighted by a factor 2 in order to account for the greater variability of a poloidal field in the vertical than in the horizontal direction. which is partly covered by the 5 km resolution aeromagnetic map of India (code 441.3).
4. Some compilations are provided at barometric altitude.
4. However. these spurious anomalies are largely removed at a later stage. when the long wavelengths are substituted with the MF5 model. However. z2 ¼ max 0. z1 . and (3) CHAMP satellite data which are included in form of the MF5 model [Maus et al. we merged the grids by LSC (see section 2). while external field disturbances with amplitudes of 100 nT already give rise to spurious magnetic anomalies. and d 1. Thus disturbed sections cannot be identified by residual amplitude..2 . starting at 0. If
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. which is partly covered by the new Russian grid (code 628. caused by stitching together small-scale surveys. areas are covered by several compilations. which we linearly interpolated to the measurement positions and added to the terrain clearance of all draped surveys. Gridded Data
[15] Most aeromagnetic surveys over land have already been combined to country-wide or even continental compilations.1.Geochemistry Geophysics Geosystems
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maus et al.2.2. We used NGDC’s ETOPO-2 surface elevation grid (http://www. This procedure may introduce spurious anomalies with half-wavelengths larger than 200 km. To deal with such edge effects. z1 and z2 are again the horizontal separation and the vertical coordinates. 1 À 1. (2) large-scale aeromagnetic and marine magnetic grids. then preparing the track line data and merging them to a combined grid. Africa and Asia (code 201. Input Data
[13] The input data fall into three different categories: (1) marine and aeromagnetic track line data. and finally replacing the longest wavelengths with MF5.html).2).gov/ mgg/global/global.3). For the accurate processing of the altitude information.noaa. We therefore used the along-track derivative of the magnetic field residual as a selection criterion. we resampled all grids to 1. These random offsets reflect inherent uncertainties at long wavelengths. (2) the GSC compilation of Eurasia (code 401.
where Rs = 100 km is the search radius. using weights which are linearly proportional to the distance from the margin. and (3) the 15 arc minute GETECH data of South America. [16] In some cases. In this definition of the weight function.2).
4. This applies to (1) the 50 km resolution ground magnetic survey of India (code 442. which are partly covered by various smaller 5 km resolution grids. 2007]. Then we computed the distance to the nearest margin for all points of every grid. we first subtracted a linear 2D trend from all smaller size grids. 1991]. while strong external field disturbances change rather rapidly.ngdc. overlapping parts of the lower quality grids were discarded.5 arc minute angular resolution using the minimum curvature algorithm (program ‘‘surface’’) of Generic Mapping Tools (GMT) [Wessel and Smith. The data sets are listed in Table 1. and it would be far beyond the scope of the WDMAM project to locate and reprocess individual surveys that contributed to these large-scale compilations. ships and aircraft move relatively slowly. In particular. If in such cases one of the compilations is known to have superior resolution or accuracy.01 on the margin and extending to a maximum value of 1.1029/2007GC001643
measurement locations in computing the misfit. Finally.2 Rs ð8Þ
[17] In order to avoid the possible loss of information in the following processing steps. However. most compilations are draped. [19] In the merging of the compilations. These compilations are mostly very well made. [18] The LSC method takes into account the exact altitude of the measurements. in order to compute the measurement altitude above the geoid. random offsets between neighboring and overlapping grids must be adjusted. respectively.0 for 200 km inland. one therefore requires a topographic model of the Earth.
3. meaning that they follow the surface topography at a constant altitude above terrain. we use the weight function
qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ À Á 1 ðd 2 þ 2ðz1 À z2 Þ2 W d1. Data Processing Steps
[14] Our data processing scheme starts with combining the existing grids to a single common grid.

Line leveling and discarding tracks with remaining high offsets lead to the middle panel. [23] Finally.5 km bins. the data were further broken into straight segments.
the derivative exceeded 100 nT/km. Similarly. the middle shows the leveled and selected data. 81 nT if only exact cross-overs are counted) and the misfit against the gridded data from 400 nT to 90 nT. we then line-leveled the 98. In fact. Several interesting inferences can be made from this figure. using a test area with strong ocean magnetic anomalies in the North Pacific. This is mostly due to the Earth’s changing main magnetic field. However. After visual inspection of the distribution of misfits.e. again using the LSC method. [24] An example of the effect of line leveling and the final merge is shown in Figure 2. we discarded the segments with a remaining between-segment misfit exceeding 550 nT. After leveling. the 20 preceding and following measurement points were discarded. plotting the misfits reveals some large outliers of segments which could not be brought
into agreement with the other data..000 track segments against each other by estimating 110. and the limited accuracy of the reference fields used for the original main field corrections.1029/2007GC001643
Figure 2. The first is that the input data are indeed seriously offset against each other. [21] In order to reduce the huge volume of data. The threshold of 100 nT for the along-track gradient was found by trial and error. or a misfit against the gridded data exceeding 500 nT.000 segments and resampled to 4 million points.000 segments and resampled to 800. The NGDC marine data consist of about 20 million points on 28.: ngdc candidate for wdmap
10. illustrated for Central America. For the subsequent line leveling. the track line data were resampled by averaging in 2. [22] Using the procedure described in section 2. The leveling and selection reduced the root-meansquare (rms) between-segment misfit from 380 nT to 130 nT (i. This threshold eliminated about 3% of the marine track line data and 9% of the Project Magnet data. Processing and merging of track line and gridded data. these offsets are of long wavelength and are removed by
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.000 tracks. It is not clear why the Project Magnet data seemed noisier than the marine data. which we broke into 91. The left panel shows the raw marine and aeromagnetic data. one may have expected the opposite. This removed about 1% of the segments.000 correction coefficients which simultaneously minimized offsets where tracks overlap with the gridded data. while the right panel shows the final map after merging with the gridded data and long-wavelength substitution. the merger with the gridded data (which also cover parts of the oceans) and the correction of the long wavelengths with the satellite model MF5 lead to the final result shown in the right panel.Geochemistry Geophysics Geosystems
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maus et al. This surprising discrepancy in data quality will have to be investigated in the run-up to the next edition of the WDMAM. This is expected for segments with strong external disturbances or segments with incorrect positions due to navigation errors. 7 million Project Magnet measurements on 3000 tracks were broken up into 7. The left panel shows the raw track line data. the leveled line data were merged with the gridded data. taking into account the altitude of the ship-borne and Project Magnet data. Finally.000 points.

between the satellite-only model MF5 and our model from the merged near-surface data. Since 2000. we used the lithospheric field
Note that the two data sources are completely independent. middle panel) one can see convincing small-scale linear features trending southeast. although they were produced largely from the same original measurements. At high degrees. We will take note of this when producing the next generation satellite lithospheric model MF6. equation (4. Adding the North American compilation introduced new problems. Degree correlation. [26] There are several ways to replace the long wavelengths of the combined grid with MF5 in the spectral domain. This should probably not have happened and needs to be investigated prior to the next map edition.1029/2007GC001643
model MF5 [Maus et al. however. Stitching together surveys and tracks collected at different times only allows for very limited control of wavelengths exceeding typical survey sizes of a few hundred kilometers. The correlation increases to an encouragingly high value of about 0. a disagreement of 10% in
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. One could even argue that MF5 should have been expanded up to the degree where the correlation peaks before decreasing to zero. If the coefficients of one model are denoted by gm and the other by km the corren n lation as a function of degree n is defined here following Langel and Hinze [1998. Here. neither for the track line data nor the gridded data. this omission had only a limited impact on the final map because the area is covered by the North American compilation. we used the original. This observation also holds in other ocean areas. Figure 3 shows the degree correlation between this model and MF5. where the track line data of an entire area were rejected because they exceeded the rms threshold. Indeed. caused by unremoved main field in the continental scale grids. By using the least squares method and eliminating the lowest Eigenvalues. as defined by equation (9). 1970]. The near-surface data exhibit strong low-degree power. [27] Another important check before replacing the long wavelengths with MF5 is to see how well their power spectra agree. the high correlation indicates that valuable small-scale signal is contained in the satellite data beyond degree 100. Fortunately. We computed this magnetic potential of the near-surface data to degree 120.: ngdc candidate for wdmap
10.6 at degree 100. Figure 4 shows the nearsurface data spectrum in comparison with MF5. the power of the near-surface data is only about 10% higher than MF5. 2007]. Substituting the Longest Wavelengths With a CHAMP Satellite Model
[25] Long wavelengths in grid and track line data are known to be highly inaccurate. rather than one of its modifications where long wavelengths were substituted with satellite magnetic models. Unfortunately. the correlation is surprisingly high. considering the different data sources and the multitude of processing steps and corrections. validating the high-degree coefficients of MF5. where line-leveled marine data often provide more accurate information than the compilations.
4. A total intensity data coverage on the sphere does not completely constrain the magnetic potential [Backus. Considering the completely different nature of the two data sets. as seen in the middle panel. We chose a processing route via the magnetic potential.. however: Off the Pacific coast of Central America (Figure 2. This is primarily due to temporal changes of the main field. one can select one of many magnetic potentials that represent the observed anomaly. Again. A problem in the line leveling is exposed for the Cayman trough. these features are strongly suppressed when adding on the North American compilation. the CHAMP satellite has been measuring the magnetic field with unprecedented accuracy.Geochemistry Geophysics Geosystems
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the line leveling. unfiltered NAMAG grid.23)] as
P m m m gn kn C ðnÞ ¼ h P À m Á2 P À m Á2 i1=2 m gn m kn ð9Þ
Figure 3. These long wavelengths are more accurately recorded by low-orbiting satellites. estimated from the latest three years of CHAMP data from August 2003 through July 2006. The ambiguity is further increased by the incomplete data coverage.3. In particular. No satellite data have been used in our grid.

The polar stereographic projections did not exhibit this problem.
4. This substitution was carried out by subtracting the near-surface model to degree 100 from each grid cell and then adding the prediction from MF5. we had discarded areas of the lower-resolution grids which were covered already by higher-resolution grids. there are equally strong parallel patterns. while excess power in the near-surface data at 400 km wavelength could be due to spurious large-scale features introduced in the stitching together of small-area surveys. GIS Flags
[29] The format definition of the WDMAM grid includes a fourth column identifying the primary data source of each grid cell.
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. North/South oriented tracks become very wide and East/West oriented tracks exceedingly thin. Grid Availability and Outlook
[32] The official WDMAM is expected to be released in July 2007 at the Meeting of the International Union of Geodesy and Geophysics in Perugia. The prime candidate for a lack of power in MF5 is the removal of genuine field in the rigorous processing of the satellite data.1029/2007GC001643
archy of the different data sets based on data resolution and accuracy should be assigned. For our final map we therefore used GMT’s Mollweide projection. but because it is the only well-surveyed area in the region. In remaining overlap areas. This has the additional advantage of showing where further data are needed for future WDMAM editions. but in the absence of measurements the grid defaults to the smooth MF5 model. 77. The blue line shows the spectrum of the final NGDC candidate map. We therefore prefer to plot the field only for areas where nearsurface data are available. Such misinterpretation is avoided if the fill-in values are not plotted as part of the map.Geochemistry Geophysics Geosystems
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maus et al. rue Claude-Bernard. As mentioned above. due to anisotropic stretching in global projections track line widths are distorted. Spectra of the near-surface-data spherical harmonic model and MF5.: ngdc candidate for wdmap
10. as well as a DVD with the digital grid and the candidate WDMAM submissions. our present flagging is somewhat arbitrary. where the mid ocean ridge stands out clearly as a positive anomaly. With the Generic Mapping Tool’s Mercator projection.
power (which amounts to even less in amplitude) is encouragingly small. However. reflecting the line leveling onto the gridded data. In future map editions a hier-
6. the lines should be equally broad for North/South and East/West oriented tracks. There will be a paper copy of the map. We decided that gridded data should have priority over track line data. The high power at low degrees in the near-surface data is primarily due to uncorrected main field. on the other hand. which avoids this distortion.
5. It is difficult to pin-point the source of this discrepancy which is probably a mix of several effects. In the grid. It should be noted. This occurs not because the ridge is particularly magnetic. This information is of course not unique in areas of overlapping data sets. Most likely. [28] Given the good spectral agreement between MF5 and the near-surface model at degree 100. to be distributed by the Commission for the Geological Map of the World.4. the power levels in the two models differ only by about 10%. [31] In plotting the final map (Figure 5). Result
[30] The final result (Figure 5) of the processing is a three arc minute angular grid of the total intensity anomaly at 5 km above the WGS84 geoid. This problem is particularly obvious in the southern Indian Ocean. that plotting these fillin values as part of the map can lead to serious misinterpretation since it is then unclear whether the field is smooth because of the geologic setting or because of inadequate data coverage.
Figure 4. we find that there is a technical difficulty in displaying single track lines. unsurveyed areas are filled with the satelliteonly model MF5 and flagged with code 13. however. we use a sharp cut-off to substitute the long wavelengths of the near-surface data with the MF5 model. Ideally. At high degrees. 75005 Paris. hopefully motivating new data collection efforts.

[35] Thus a more complete spatial coverage by marine and aeromagnetic data. offers the scope for further significant improvements in upcoming WDMAM editions. Richard Blakely and Erwan
Thebault. with plans to produce updates of the map and grid every couple of years.getech.com/downloads/ WDMAM.html).Geochemistry Geophysics Geosystems
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maus et al. The top panel shows a Mollweide projection with cut-off at 70° latitude. The digital grid of the NGDC candidate for WDMAM is already publicly available at http:// geomag. [33] The WDMAM is an ongoing project.org/cgi-bin/erda. Following in 2010 is the European Space Agency’s Swarm mission.
Acknowledgments
[36] We thank two referees. esa. for various reasons. creating momentum to conduct further aeromagnetic surveys and help to complete the global coverage. for numerous suggestions that helped to improve
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. 2006]. This will further improve lithospheric magnetic anomaly maps by providing direct measurements of magnetic field gradients [Maus et al.
France. additional data will be acquired for presently uncovered areas..cgi?n=735 as a permanent archive. a constellation comprising 3 satellites (http://www. As part of these updates. The final NGDC WDMAM candidate grid.html and at http:// earthref. Furthermore. [34] Further significant improvements in accuracy and resolution can be expected at long wavelengths
of the spatial spectrum which is supplied by loworbiting satellites. together with better control of the long wavelengths from new satellite missions.org/models/wdmam.1029/2007GC001643
Figure 5. It is our hope that the WDMAM will enjoy widespread usage.: ngdc candidate for wdmap
10. The polar stereographic projections in the bottom two panels extend down to 40° in latitude.int/esaLP/LPswarm. a package for visualization of the map in NASA World Wind can be downloaded from http://www. Some of these areas have already been surveyed but the data are not readily accessible. The CHAMP mission is expected to continue providing excellent quality data at solar minimum conditions and at steadily decreasing altitudes up to the year 2009.